Properties of Cosmic Helium Isotopes Measured by the Alpha Magnetic Spectrometer

Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of 3 He and 4 He fluxes are presented. The measurements are based on 100 million 4 He nuclei in the rigidity range from 2.1 to 21 GV and 18 million 3 He from 1.9 to 15 GV collected from May 2011 to November 2017. We observed that the 3 He and 4 He fluxes exhibit nearly identical variations with time. The relative magnitude of the variations decreases with increasing rigidity. The rigidity dependence of the 3 He = 4 He flux ratio is measured for the first time. Below 4 GV, the 3 He = 4 He flux ratio was found to have a significant long-term time dependence. Above 4 GV, the 3 He = 4 He flux ratio was found to be time independent, and its rigidity dependence is well described by a single power law ∝ R Δ with Δ ¼ − 0 . 294 (cid:2) 0 . 004 . Unexpectedly, this value is in agreement with the B/O and B/C spectral indices at high energies.

Jülich Supercomputing Centre and JARA-FAME, Research Centre Jülich, 52425 Jülich, Germany Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of 3 He and 4 He fluxes are presented. The measurements are based on 100 million 4 He nuclei in the rigidity range from 2.1 to 21 GV and 18 million 3 He from 1.9 to 15 GV collected from May 2011 to November 2017. We observed that the 3 He and 4 He fluxes exhibit nearly identical variations with time. The relative magnitude of the variations decreases with increasing rigidity. The rigidity dependence of the 3 He= 4 He flux ratio is measured for the first time. Below 4 GV, the 3 He= 4 He flux ratio was found to have a significant long-term time dependence. Above 4 GV, the 3 He= 4 He flux ratio was found to be time independent, and its rigidity dependence is well described by a single power law ∝ R Δ with Δ ¼ −0.294 AE 0.004. Unexpectedly, this value is in agreement with the B/O and B/C spectral indices at high energies. DOI: 10.1103/PhysRevLett.123.181102 Helium nuclei are the second most abundant cosmic ray. They consist of two isotopes, 4 He and 3 He. 4 He are thought to be mainly produced and accelerated in astrophysical sources, while 3 He are overwhelmingly produced by the collisions of 4 He with the interstellar medium. The precise knowledge of the rigidity dependences of the helium isotope fluxes and their ratio provides important information on the sources, acceleration, and propagation of cosmic rays [1].
Helium ( 3 He, 4 He) interaction cross sections with the interstellar medium (p, He) are significantly smaller than those of heavier nuclei (Li, Be, B, C, N, O, …). Therefore, helium travels larger distances, probing a larger Galactic volume. Explicitly, the 3 He= 4 He ratio probes the properties of diffusion at larger distances [2]. 3 He is produced by the fragmentation of 4 He with the interstellar medium, whereas Li, Be, and B are produced by multiple fragmentation channels of many heavy nuclei with the interstellar medium [3]. Therefore, the 3 He= 4 He flux ratio provides unique input to cosmic-ray propagation models [4], distinctly different from the commonly studied secondary/primary ratios of heavier elements such as B/C and B/O [5][6][7].
Previously, the flux of helium nuclei has been measured by AMS based on 90 million events collected during the first 5 yr of operation, revealing an unexpected hardening at high energies [8]. In addition, AMS reported the precise measurement of the electron, positron, proton, and helium fluxes as functions of time [9,10].
The large acceptance and high precision of AMS allow the accurate measurements of temporal variation of 3 He and 4 He fluxes for the first time. Time correlations of different particle (e þ , e − , p, 3 He, 4 He) flux variations are expected by models of cosmic-ray transport in the heliosphere [11]. The relative magnitude of these variations decreases with increasing rigidity. This is because the cosmic-ray transport in the heliosphere is rigidity dependent and related to changes in solar activity [12].
There are no previous measurements of the 3 He= 4 He ratio as a function of rigidity. At lower energies and with larger errors, there have been measurements of helium isotope fluxes and their ratio as functions of the kinetic energy per nucleon [13].
In this Letter, precision measurements of the 3 He and 4 He fluxes and the 3 He= 4 He flux ratio are presented from 1.9 to 15 GV for 3 He, from 2.1 to 21 GV for 4 He, and from 2. He to percent level accuracy. The total flux error at 10 GV is 2.5% for 3 He and 2% for 4 He.
Selection.-In the first 6.5 yr of operation, AMS has collected 1.07 × 10 11 cosmic-ray events. The collection time used in this analysis includes only those seconds during which the detector was in normal operating conditions and, in addition, the AMS was pointing within 40°o f the local zenith and the International Space Station (ISS) was outside of the South Atlantic Anomaly. Because of the influence of the geomagnetic field, the collection time for galactic cosmic rays increases with rigidity, reaching 1.31 × 10 8 s at 20 GV. Helium events are required to be downward going and to have a reconstructed track in the inner tracker which passes through L1 and a reconstructed velocity from the TOF > 0.3. Track fitting quality criteria such as a χ 2 =d:o:f: < 10 in the bending coordinate are applied, similar to Ref. [8]. For events with a velocity above the Čerenkov threshold, we require additional quality criteria such as the number of hits in the Čerenkov ring > 4, compatible velocity measurements in the TOF and RICH, i.e., j1 − β TOF =β RICH j < 0.05, and the charge measured in the RICH > 1.2.
To select only primary helium events [8,24] with the same exposure time for both He isotopes, the measured velocity of the particles is required to be greater than that of 3 He with a rigidity equal to 1.2 times the maximum geomagnetic cutoff within the AMS field of view. The cutoff is calculated by backtracing particles [25] from the top of AMS out to 50 Earth radii using the most recent International Geomagnetic Reference Field [26].
Because of the multiple independent measurements of the charge, the selected helium sample contains a negligible background (< 10 −3 ) of particles with Z > 2 at the top of the AMS [8]. The additional background in the 3 He sample is due to the fragmentation of 4 He → 3 He within the AMS materials, mostly carbon and aluminum [8].
To estimate this background, we used the reaction 4 He þ ðC; AlÞ → 3 H, that has the same cross section as 4 He þ ðC; AlÞ → 3 He [4,27]. This is illustrated in Fig. S1 in Supplemental Material [23], which shows the mass distribution of events interacting between L1 and L2 for data and MC simulation in the velocity range 0.9721 < β < 0.9954. As seen, the peaks of protons, deuterons, and tritons are clearly observable, and the MC simulation agrees well with the data. The corresponding background of 3 He from 4 He interactions in the AMS material was estimated from the MC simulation to be less than 10% of the 3 He sample in the entire rigidity range, with uncertainties of < 1% for the 3 He flux.
To identify the He isotopes, a procedure based on the unfolding of the rigidity distribution [28] is used. After unfolding with the rigidity resolution function, the top of the instrument rigidity distribution of each isotope and the number of corresponding events are determined from velocity bins of width ∼0.2Δβ. Examples of rigidity distributions and results of unfolding are presented in Fig. S2 in Supplemental Material [23] for velocity bins of the TOF, RICH-NaF, and RICH-Agl. Finally, the rate distribution (Γ) in rigidity is obtained by dividing the number of events in each velocity bin by the corresponding velocity-dependent exposure time.
Analysis.-The fluxes of the helium isotopes are measured as functions of the rigidity in 26 bins from 1.92 to 21.1 GV chosen according to Ref. [8]. The isotropic flux Φ A i for an isotope of atomic mass number A in the ith rigidity bin ðR i ; R i þ ΔR i Þ is given by PHYSICAL REVIEW LETTERS 123, 181102 (2019) where Γ A i is the sum of the unfolded rates in rigidity bin i, A A i the effective acceptance, ϵ A i the trigger efficiency, and ΔR i the bin width.
Extensive studies were made of the systematic errors. The systematic errors that affect the determination of Γ A i include the uncertainties due to the resolution functions in the velocity and rigidity used in the unfolding procedure. The TOF velocity resolution function Δð1=βÞ has a Gaussian core of width 0.02. The velocity resolution functions of the RICH-NaF and RICH-Agl are similar; the RICH-Agl has a pronounced Gaussian core characterized by a width of 7 × 10 −4 at β ¼ 1 and decreases with decreasing velocity to 6.3 × 10 −4 at β ∼ 0.953. The velocity resolution functions of TOF and RICH are obtained from the MC simulation and validated at β ¼ 1 with data, as shown in Fig. S3 in Supplemental Material [23]. The rigidity resolution function, determined from the MC simulation, has been extensively verified with the data [8]. The systematic errors due to uncertainties in the rigidity resolution functions have been estimated by varying the width of the resolution function by 10%. The systematic error from the determination of Γ A i on the 3 He flux is 3% at 2 GV, is 1% from 3 to 10 GV, and increases up to 4.5% at 15 GV. For the 4 He flux, it is 4% below 3 GV, is 1% from 4 to 15 GV, and increases up to 3% at 21 GV.
Other sources of systematic error include uncertainties in the trigger efficiency, in the geomagnetic cutoff, and in the acceptance.
The trigger efficiency of 3 He and 4 He has been measured following a procedure similar to Ref. [8]. The systematic error on the fluxes associated with the trigger efficiency uncertainties is < 0.7% for 3 He and < 0.2% for 4 He over the entire rigidity range.
The geomagnetic cutoff factor was varied from 1.0 to 1.4, resulting in a negligible systematic uncertainty ð<0.1%Þ in the whole rigidity range.
The effective acceptances A A i were calculated from the MC simulation and then corrected for differences between the data and simulated events related to (a) event reconstruction and selection, namely, in the efficiencies of track finding, charge determination, tracker quality cuts, and velocity quality cuts, and (b) inelastic interactions of helium nuclei in the AMS material. The total correction to the effective acceptances was found to be < 10% over the entire rigidity range. The systematic error on the 3 He and 4 He fluxes associated to (a) has been found by a comparison between the data and MC simulation to be 2.5% below 2 GV, to be 3.5% between 2 and 7 GV, and to decrease to 1.5% above 7 GV. The systematic error on (b) has been studied in detail in Ref. [8]. The corresponding systematic error on the 3 He flux was found to be 1.5% and, for 4 He, 1% [22].
The variations of the trigger and reconstruction efficiencies were monitored as functions of time. A time-dependent systematic error due to the variations of trigger and reconstruction efficiencies for different time periods was estimated to be 1% in the whole rigidity range for both the 3 He and 4 He fluxes. All the other systematic errors discussed above are time independent.
Results.-The 3 He and 4 He fluxes are measured as functions of the rigidity from May 2011 to November 2017 in 21 time periods of four Bartels rotations (108 days) each. The fluxes and the flux ratio are presented in Tables I-XXI in Supplemental Material [23], including statistical and systematic errors. For the fluxes, the contributions of individual sources to the systematic error are added in quadrature to obtain the total systematic uncertainty. The sum of the two fluxes is consistent with Refs. [8,9] over the same time periods. For the 3 He= 4 He flux ratio, the correlation of the systematic errors is taken into account to evaluate the total systematic error. Figure 1 shows the 3 He and 4 He fluxes as functions of time for five characteristic rigidity bins. As seen, both spectra exhibit nearly identical variations with time. The relative magnitude of the variations decreases with increasing rigidity; as seen in Fig. 1(a), 2.15 < R < 2.40 GV, the maximum and minimum are different by a factor of 2, whereas in Fig. 1(e), 14.1 < R < 15.3 GV, the difference is 10%. The observed variations are compatible with those observed by AMS in the proton flux [9] and in the electron and positron fluxes [10]. Together, these provide important insights on the dynamics of solar modulation. Figure 2 shows the 3 He= 4 He flux ratio as a function of time for the same five rigidity bins. As seen, at low rigidities the 3 He= 4 He flux ratio shows two distinct time behaviors similar to the p=He flux ratio in Fig. 4 in Ref. [9]. To characterize the time dependence of the 3 He= 4 He flux ratio at low rigidities, a procedure similar to the one described in Ref. [9] was used. We performed fits of the flux ratio as a function of time for each rigidity bin according to where r i ðtÞ is the 3 He= 4 He flux ratio for rigidity bin i as a function of time t, a i is the average 3 He= 4 He flux ratio from May 2011 tot, and b i is the slope of the time variation aftert. Below 4 GV, the fits yield at compatible with the average transition time found in the p=He flux ratio of (February 28, 2015)AE42 days [9]. The results of the fits are also shown (dashed red lines) in Fig. 2 fort fixed to February 28, 2015 [9]. As seen, the 3 He= 4 He flux ratio exhibits a long-term time variation at low rigidities that gradually decreases with increasing rigidities. Above 4 GV, the ratio is found to be consistent with a constant value at the 95% C.L. The measured 3 He and 4 He time-averaged fluxes and the corresponding 3 He= 4 He flux ratio for the 6.5 yr period are reported in Table XXII in Supplemental Material [23] as a function of the rigidity including statistical and systematic errors. Figure S4 in Supplemental Material [23] shows the time-averaged 3 He and 4 He fluxes together with the range of time variation.
To compare with previous experiments [13], the 3 He and 4 He fluxes and their ratio have also been measured using the same unfolding procedure described above from 0.5 to 10 GeV=n as functions of the kinetic energy per nucleon,  He ratio with total errors as a function of the kinetic energy per nucleon, together with earlier experiments [13]. The dashed line shows the prediction of the GALPROP model [29] with the average solar modulation, in the force-field approximation [30], corresponding to the data collection period. their ratio, including statistical and systematic errors, are reported in Table XXIII in Supplemental Material [23] as functions of E K . The 3 He= 4 He ratio as a function of the kinetic energy per nucleon is shown in Fig. 3 together with earlier experiments and the GALPROP model [29] with the average solar modulation, in the force-field approximation [30] corresponding to the data collection period.
The AMS result provides a precision measurement and covers a large energy range.
The time-averaged 3 He= 4 He flux ratio as a function of rigidity is shown in Fig. 4(a). Above 4 GV, the 3 He= 4 He flux ratio is time independent and is well described with a single power law, CðR=4 GVÞ Δ . A fit to the data yields Δ ¼ −0.294 AE 0.004 and C ¼ 0.1476 AE 0.0004, with χ 2 =d:o:f: ¼ 15.7=13. Below 4 GV, to study the time and rigidity dependence of the 3 He= 4 He flux ratio, fits to CðR=4 GVÞ δ for each period of four Bartels rotations were performed. The results of the fits are shown as a shaded band in Fig. 4(a) and yield an average δ of hδi ¼ −0.21 AE 0.02 with a time variation of AE0.05. Different from the B/O and B/C flux ratios, which show a maximum around 4 GV [see Figs. S9(c) and S10(c) in Ref. [6]], the 3 He= 4 He flux ratio is steadily decreasing with the rigidity. Because of different propagation volumes and different inelastic interaction cross sections of He, B, C, and O, the B/O and B/C flux ratio rigidity dependence may be different from the 3 He= 4 He flux ratio rigidity dependence, and this provides important information to discriminate among different cosmic-ray models [1,2,4]. The comparison of our data with models will be presented in a forthcoming publication [31]. Figure 4(b) shows the 3 He= 4 He flux ratio spectral index as a function of R for four independent rigidity bins. As seen, above 4 GV, the spectral index shows no dependence with rigidity with an average value of Δ ¼ −0.294 AE 0.004. The extrapolation of Δ to higher energies is shown as a dotted line. The B/O and B/C flux ratio spectral indices [5,6] are shown as blue filled squares and blue open squares, respectively. As seen, the 3 He= 4 He spectral index extrapolation to the highest energies is in agreement with the B/O and B/C spectral indices.
In conclusion, precision measurements of the cosmic-ray 3 He and 4 He isotope fluxes and their ratio are presented as functions of rigidity from 1.9 to 15 GV for 3 He, from 2.1 to 21 GV for 4 He, and from 2.1 to 15 GV for the 3 He= 4 He flux ratio based on 100 million 4 He and 18 million 3 He nuclei collected by AMS from May 2011 to November 2017. Below 4 GV, the 3 He= 4 He flux ratio shows a significant long-term time dependence. Different from the B/C and B/O flux ratios, which show a maximum around 4 GV, the 3 He= 4 He flux ratio was found to be decreasing with rigidity; below 4 GV, the ratio is well described by a single power law ∝ R δ with hδi ¼ −0.21 AE 0.02 and a time variation of AE0.05. Above 4 GV, the 3 He= 4 He flux ratio was found to be time independent, and its rigidity dependence is well described by a single power law ∝ R Δ with Δ ¼ −0.294 AE 0.004. Unexpectedly, this value is in good agreement with the B/O and B/C spectral indices at high energies.
We are grateful for important physics discussions with Pasquale Blasi, Fiorenza Donato, Jonathan Ellis, Jonathan Feng, Mischa Malkov, Igor Moskalenko, and Subir Sarkar. We thank former NASA Administrator Daniel S. Goldin for He= 4 He flux ratio spectral index (red points) as a function of R. As seen, above 4 GV, the spectral index shows no dependence with rigidity (green band). The extrapolation of Δ to higher energies is shown (green dotted line). The B/O (blue filled squares) and B/C (blue open squares) flux ratio spectral indices [5,6] are also shown. As seen, the 3 He= 4 He spectral index extrapolated to the highest energies is in good agreement with the B/O and B/C spectral indices.